Now we will discuss the exchange interactions in ferromagnetic
bodies. This interaction should be analyzed by means of quantum
theory, since it strongly concerns with spin-spin interactions.
More specifically, on a scale in the order of the atomic scale,
the exchange interaction tends to align neighbor spins. In view of
a continuum average analysis in terms of magnetization vector
field, we expect that the exchange interactions tends to produce
small uniformly magnetized regions, indeed observed experimentally
and called magnetic domains. In this respect, the existence
of domains [8] was postulated by Weiss in the early 1900s
to explain the inverse temperature dependance of susceptibility
for ferromagnetic materials investigated by Curie. This theory was
partially validated by the work of Barkhausen (1915), in which the
emergence of irreversible jumps in magnetization reversal was
connected to the Weiss domains. Successively, experimental
observations [9] based on Faraday and Kerr effect
measurements, definitely stated the existence of magnetic domains.
However, in 1931 Heisenberg [10] described
ferromagnetic bodies in terms of exchange interactions, justifying
the Weiss theory on molecular field. In the following sections a
brief summary of paramagnetism and classical Weiss molecular field
is presented before deriving the phenomenological expression of
exchange free energy used in micromagnetics.
Subsections